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Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice
dc.contributor.author | Van Vleck, Erik S. | |
dc.contributor.author | Mallet-Paret, John | |
dc.contributor.author | Cahn, John W. | |
dc.date.accessioned | 2015-04-02T16:10:26Z | |
dc.date.available | 2015-04-02T16:10:26Z | |
dc.date.issued | 1999-03-05 | |
dc.identifier.citation | Van Vleck, Erik., Mallet-Paret, John., Cahn, John W. "Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice." (1999) SIAM J. Appl. Math., 59(2), 455–493. (39 pages). http://dx.doi.org/10.1137/S0036139996312703. | en_US |
dc.identifier.uri | http://hdl.handle.net/1808/17284 | |
dc.description | This is the published version, also available here: http://dx.doi.org/10.1137/S0036139996312703. | en_US |
dc.description.abstract | We consider infinite systems of ODEs on the two-dimensional integer lattice, given by a bistable scalar ODE at each point, with a nearest neighbor coupling between lattice points. For a class of ideal nonlinearities, we obtain traveling wave solutions in each direction $e^{i\theta}$, and we explore the relation between the wave speed c, the angle $\theta$, and the detuning parameter a of the nonlinearity. Of particular interest is the phenomenon of "propagation failure," and we study how the critical value $a=a^*(\theta)$ depends on $\theta$, where $a^*(\theta)$ is defined as the value of the parameter a at which propagation failure (that is, wave speed c=0) occurs. We show that $a^*:\Bbb{R}\to\Bbb{R} is continuous at each point $\theta$ where $\tan\theta$ is irrational, and is discontinuous where $\tan\theta$ is rational or infinite. | en_US |
dc.publisher | Society for Industrial and Applied Mathematics | en_US |
dc.subject | traveling waves | en_US |
dc.subject | propagation failure | en_US |
dc.subject | anisotropy | en_US |
dc.subject | Allen--Cahn equation | en_US |
dc.title | Traveling Wave Solutions for Systems of ODEs on a Two-Dimensional Spatial Lattice | en_US |
dc.type | Article | |
kusw.kuauthor | Van Vleck, Erik | |
kusw.kudepartment | Mathematics | en_US |
dc.identifier.doi | 10.1137/S0036139996312703 | |
kusw.oaversion | Scholarly/refereed, publisher version | |
kusw.oapolicy | This item does not meet KU Open Access policy criteria. | |
dc.rights.accessrights | openAccess |